摘要
针对第二代小波尺度函数无显式表达式的缺点,提出采用PsdVoigt2函数进行拟合的方法,根据小波有限元及第二代小波理论,利用第二代小波尺度函数取代传统有限元多项式插值函数,通过转换矩阵将小波插值系数转换到物理空间,构造出形函数,并利用该方法构造一系列杆、梁单元。通过不同算例对构造的第二代小波杆、梁单元进行精度验证。计算结果表明,构造的第二代小波单元在求解变形和应变时精度较高,丰富了小波有限元单元库。
PsdVoigt2 function was used to fit SGW function,and a series of bar beam elements based on the theory of SGW and wavelet finite element were constructed. Traditional finite element polynomial interpolation was replaced by the SGW scaling function,and transformation matrix was utilized to transform wavelet interpolation coefficients to physical space,then the shape function and a series of bar beam elements were constructed. The precision of constructed bar beam elements using SGW scale function as the interpolation function was verified by a series of calculation cases. The calculation results show that the SGW-based element has good precision in calculating the deformation and strain. The SGW-based bar beam element enriches the element library of wavelet-finite element method.
出处
《中国石油大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2014年第5期135-141,共7页
Journal of China University of Petroleum(Edition of Natural Science)
基金
国家重大科技专项(2011ZX05038)
中央高校基本科研业务费专项资金(12CX06063A)
关键词
第二代小波
小波有限元
一维单元
单元构造
SGW
wavelet-finite element
one-dimensional element
construction of elements
